Finite Group Databasebeta

← #13073691

Subgroups — #13073691

Order 1408.

696 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67000C212yesmaximal, complemented
2C2×#66948C212yesmaximal, complemented
3C11×#395C211yesmaximal, characteristic, complemented
4#10622604C211yesmaximal, characteristic, complemented
5#10622603C212yesmaximal, complemented
6#10622601C211yesmaximal, characteristic, complemented
7#10622284C212yesmaximal, complemented
8#10622279C212yesmaximal, complemented
9#10622278C212yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C22×D44C2212yes—
13C22×D44C2212yes—
14C22×D44C2211yescharacteristic
15C22×C4×D11C2212yes—
16C2×C11×C4⋊C4C2212yes—
17C2×C11×C4⋊C4C2211yescharacteristic
18#67000—28no—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4×Dic11C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28#66948—28no—
29C11×#95C2211yescharacteristic
30C11×#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2211yescharacteristic
33C23×D11C2312yes—
34C23×D11C2312yes—
35C2×Q8×C11—24no—
36C2×Q8×C11—41no—
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C2×D44—24no—
45C2×D44—24no—
46C2×D44—24no—
47C2×D44—24no—
48C2×D44—22no—
49C2×D44—24no—
50C2×D44—41no—
51C2×D44—41no—
52C2×D44—42no—
53C2×D44—42no—
54C2×D44—41no—
55C2×C4×D11—24no—
56C2×C4×D11—24no—
57C2×C4×D11—42no—
58C11×C4⋊C4—24no—
59C11×C4⋊C4—41no—
60(C2×D11)⋊C4—24no—
61(C2×D11)⋊C4—24no—
62(C2×D11)⋊C4—24no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4D418yescomplemented
67C4×Dic11—24no—
68C4×Dic11—41no—
69#2555—111nomaximal, Sylow
70C23×C11C2411yescharacteristic
71C22×D11—22no—
72C22×D11—22no—
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—22no—
76C22×D11—22no—
77C22×D11—22no—
78C22×D11—22no—
79C22×D11—22no—
80C22×D11—22no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11C2×D414yes—
85Q8×C11—44no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11C2×D414yes—
97C2×C4×C11#4112yes—
98C2×C4×C11#4114yes—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11C2×D414yes—
105D44—48no—
106D44—48no—
107D44—44no—
108D44—44no—
109C4×D11—48no—
110C2×#124—112no—
111C2×#121—112no—
112#395D1111yescharacteristic, complemented
113#394—111no—
114#392—112no—
115#390—111no—
116#388—112no—
117#386—112no—
118C4×C22⋊C4—112no—
119C22×C11C22×D412yes—
120C22×C11C2×#4111yescharacteristic
121C22×C11C2×#4112yes—
122C22×C11H(5,𝔽2)11yescharacteristic
123C22×C11H(5,𝔽2)11yescharacteristic
124C2×D11—24no—
125C2×D11—24no—
126C2×D11—24no—
127C2×D11—42no—
128C2×D11—42no—
129C2×D11—42no—
130C2×D11—42no—
131C2×D11—42no—
132C2×D11—42no—
133C2×D11—42no—
134C2×D11—42no—
135C2×D11—42no—
136C2×D11—42no—
137C2×D11—42no—
138C4×C11—22no—
139C4×C11—24no—
140C4×C11—24no—
141C4×C11—41no—
142C4×C11—41no—
143Dic11—24no—
144Dic11—42no—
145C22×Q8C2×D1111yescharacteristic
146C22×D4—111no—
147C22×D4—112no—
148C22×D4—112no—
149C22×D4—111no—
150C23×C4—112no—
151#124—228no—
152#121—228no—
153C2×C4⋊C4C2×D1112yes—
154C2×C4⋊C4C2×D1111yescharacteristic
155C2×C22⋊C4—112no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4—112no—
158C2×C22⋊C4—112no—
159C2×C22⋊C4—112no—
160C2×C22⋊C4—112no—
161C2×C22⋊C4—112no—
162C2×C42—112no—
163C2×C42—111no—
164#95—112no—
165#95—111no—
166#95C2×D1112yes—
167#95C2×D1111yescharacteristic
168C2×C11#53212yes—
169C2×C11#53811yescharacteristic
170C2×C11D4211yescharacteristic
171C2×C11#54612yes—
172C2×C11#55511yescharacteristic
173D11—44no—
174D11—82no—
175C24—112no—
176C24—112no—
177C2×Q8—24no—
178C2×Q8—41no—
179C2×D4—224no—
180C2×D4—224no—
181C2×D4—224no—
182C2×D4—224no—
183C2×D4—222no—
184C2×D4—224no—
185C2×D4—441no—
186C2×D4—442no—
187C2×D4—441no—
188C2×D4—442no—
189C2×D4—441no—
190C22×C4—112no—
191C22×C4—112no—
192C22×C4—224no—
193C22×C4—224no—
194C22×C4—442no—
195C22×C4C22×D1111yescharacteristic
196C22×C4C22×D1111yescharacteristic
197C22×C4C22×D1112yes—
198C22×C4C22×D1112yes—
199C22×C4C22×D1111yescharacteristic
200C4⋊C4—24no—
201C4⋊C4—41no—
202C22⋊C4—118no—
203C22⋊C4—224no—
204C22⋊C4—224no—
205C22⋊C4—224no—
206C22⋊C4—224no—
207C22⋊C4—224no—
208C22⋊C4—224no—
209C42—224no—
210C42—441no—
211C11#255511yescharacteristic, complemented, Sylow
212C23—114no—
213C23—222no—
214C23—222no—
215C23—222no—
216C23—222no—
217C23—222no—
218C23—222no—
219C23—222no—
220C23—222no—
221C23—222no—
222C23—222no—
223C23—222no—
224C23—222no—
225C23—222no—
226C23C23×D1111yescharacteristic
227Q8—44no—
228D4—448no—
229D4—448no—
230D4—444no—
231D4—444no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—114no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—448no—
249C2×C4D4×D1114yes—
250C2×C4#434312yes—
251C2×C4#434314yes—
252C22—224no—
253C22—224no—
254C22—224no—
255C22—442no—
256C22—442no—
257C22—442no—
258C22—442no—
259C22—442no—
260C22—442no—
261C22—442no—
262C22—442no—
263C22—442no—
264C22—442no—
265C22—442no—
266C22C2×D4×D1112yes—
267C22#6703711yescharacteristic
268C22C2×#434311yescharacteristic
269C22C2×#434312yes—
270C22#6704211yescharacteristic
271C4—24no—
272C4—24no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—224no—
277C4—442no—
278C2—444no—
279C2—882no—
280C2#1062312111yescharacteristic
281C2#1062316112yes—
282C2#1062317511yescharacteristic
283C2#1062325612yes—
284C2#1062326511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#395C2
hypercenter#395D11
hypocenterC11#2555
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#67000C2semidirect
2. C2×#66948C2semidirect
3. C11×#395C2semidirect
4. #10622604C2semidirect
5. #10622603C2semidirect
6. #10622601C2semidirect
7. #10622284C2semidirect
8. #10622279C2semidirect
9. #10622278C2semidirect
66. (C2×D11)⋊C4D4semidirect
112. #395D11semidirect
211. C11#2555semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#670002
C2×#669482
C11×#3952
#106226042
#106226032
#106226012
#106222842
#106222792
#106222782
#255511